TELECOMMUNICATIONS AND RADIO ENGINEERING - 2010 Vol. 69,
No 8 		 

 

 

 

Application of Fractional Operators to Describing Boundaries in the Scattering Problems


E.I. Veliev & Ì.V. Ivakhnychenko
A. Usikov Institute of Radio Physics and Electronics,
National Academy of Sciences of Ukraine
12, Academician Proskura St., Kharkiv 61085, Ukraine
Address all correspondence to E.I. Veliev E-mail: veliev@kharkov.ua

Ò.Ì. Ahmedov
Institute of Mathematics, National Academy of Sciences of Azerbaijan
9, F. Agaev St., Baku 1141, Azerbaijan

Abstract
The possibility is analyzed for applying fractional operators in the problems of electromagnetic wave reflection from plane boundaries. The fractional derivative and fractional curl operator are considered, which are obtained as a result of fractionalization of the ordinary derivation and curl operators. The fractional curl operator can be used for describing the polarization reversal effect for the wave reflected from a biisotropic layer or boundary characterized by anisotropic impedance boundary conditions. The order of the fractional curl operator is determined through the constitutive parameters of the problem under consideration. Boundary conditions with a fractional derivative generalize the condition for perfectly electric and perfectly magnetic conducting boundaries. Application of the fractional boundary conditions (FBC) to modeling wave reflection from plane boundaries is analyzed. The scattering properties of a strip with FBC and of an impedance strip are compared by the example of the problem of diffraction at a strip of a finite width. Expressions have been derived which relate the fractional order with the impedance. It is shown that FBC can be used over a wide range of parameter variation for the wave reflection simulation from impedance boundaries, as well as from a dielectric layer. The FBC correspond to impedance boundaries with a pure imaginary value of the impedance. Also the specific features shown by the scattering characteristics of a strip with FBC, which are associated with its “superwave” properties, are analyzed.

KEY WORDS: fractional derivative, fractional curl operator, boundary condition, diffraction



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pages 653-668

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